olymmath

HMMT 2016 U2

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Sherry is waiting for a train. Every minute, there is a 75%75 \% chance that a train will arrive. However, she is engrossed in her game of sudoku, so even if a train arrives she has a 75%75 \% chance of not noticing it (and hence missing the train). What is the probability that Sherry catches the train in the next five minutes?

Dataset text NuminaMath olympiads. Quoted with source.

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1-\left(\frac{13}{16}\right)^{5}

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